International Cricket Council general manager Dave Richardson said on Thursday the world governing body would soon be making its appointments for series starting after April 1.
"England and New Zealand are both teams who seem to be happy with him," Richardson said in a telephone interview from the ICC's Dubai headquarters. "There wouldn't be anything standing in the way of appointing him to that series."
Hair, 55, was dropped from the ICC's Elite umpires' panel for his role in the 2006 Oval Test between England and Pakistan.
Pakistan became the first team to forfeit a Test when they refused to return to the field after tea on the fourth day of the fourth Test because they had been penalised five runs for ball tampering.
On Tuesday, the ICC announced Hair had been reappointed to the panel after undergoing a rehabilitation course which included a university course in Sydney.
The decision has outraged Pakistan authorities, who made it clear after The Oval Test that they had lost confidence in Hair. Richardson said the ICC would take Pakistan's reaction into account when appointing Hair to international matches.
"We have always followed a pretty pragmatic approach, cricket being what it is with teams getting a bee in their bonnet about a particular umpire," he said.
"It's not the first time that's happened. We try to make the appointments which we think will be best for that series. I think we should continue to do that.
"I think it is sensible to take the pragmatic approach and to give him an opportunity against teams where the pressure won't be as high."
‘No drastic change’
Hair has made it clear his umpiring attitude will not change drastically but admitted that he has been learning a few things to improve his communication, adds PTI from Sydney.
“It caused me a lot of stress, I suppose it caused a lot of people some stress along the way.
“The laws now have been changed to take those decisions out of the hands of the umpires and I fully support the way that that’s going to happen in future. So, it’s time to move on,” Hair said of his time away from the Elite Panel.
Hair said his new innings would focus on better communication on the field. The Aussie added he would look to get more involved in on-field proceedings after resuming his job.